Blind deconvolution of quadratic time-frequency representations of musical signals for reverberation feature extraction.

Abstract

An acoustic space is uniquely characterized by its reverberant behavior. Due to the complexity of the multiple reflections and diffraction of sound in an enclosure, currently available system identification algorithms cannot effectively estimate the impulse response of a concert hall simply from musical recordings in that space. This paper reports the use of blind image deconvolution methods to construct echo patterns from quadratic time-frequency representations of reverberant recordings of music. First, a quadratic time-frequency analysis is performed to decompose the musical signal into its constituent harmonic components. Quadratic time-frequency analysis methods are known to give enhanced resolution in the time-frequency plane in comparison to conventional Fourier analysis. Reverberant features then appear as blur in the time-frequency plane, which can be estimated by employing the methods of blind deconvolution of this “image” of the sound. The proposed algorithm retrieves both the blur pattern, which corresponds to the reverberation echogram, and the direct acoustic signal. By choosing the time-frequency frame scale and smoothing window, a multi-resolution analysis of the underlying acoustic impulse response is obtained. Various quadratic time-frequency analysis methods are evaluated and their relative performance is reported. The proposed methods are also compared to existing dereverberation algorithms.